Question

Point A(8,6)and B(x,10) lie on the circle whose centre is (4,6) then find the value of x

Answer 1

Step-by-step explanation:

AP (8,6)

B(x,10)

Ratio = 1:1

(4,6) = (8+2/2), (6+10/2)

(4,6) = (8+x/2) , (8)

8+x/2 = 4

8+x=8

x=0

Answer 2

Concept:

Distance = D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given:

A (8,6)

B(x,10)

Centre(4,6)

Find:

The value of x.

Solution

Let the centre be C.

C = (4,6)

Since the radius if the circle will remain same,

AC = BC

AC = √ (8 - 4)² + (6 - 6)²

AC = √4²

AC = 4 units.

BC = √(x - 4 )² + (10 - 6)²

√(x - 4 )² + 4² = 4

x² + 16 - 8 x + 16 = 16

x² + 16 - 8 x = 0

x² - 4 x - 4 x + 16 = 0

x (x - 4) - 4 (x - 4) = 0

(x - 4 )² = 0

x - 4 = 0

x = 4 units.

Therefore, the value of x is 4 units.

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